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Problem vector equation of the plane r = i − j + λ ( i + j + k ) + μ ( i − 2 j + 3 k ) \mathbf{r} = \mathbf{i} - \mathbf{j} + \lambda(\mathbf{i} + \mathbf{j} + \mathbf{k}) + \mu(\mathbf{i} - 2\mathbf{j} + 3\mathbf{k}) r = i − j + λ ( i + j + k ) + μ ( i − 2 j + 3 k ) r ⋅ ( 5 i − 2 j + 3 k ) = 7 \mathbf{r} \cdot (5\mathbf{i} - 2\mathbf{j} + 3\mathbf{k}) = 7 r ⋅ ( 5 i − 2 j + 3 k ) = 7 r ⋅ ( 5 i + 2 j − 3 k ) = 7 \mathbf{r} \cdot (5\mathbf{i} + 2\mathbf{j} - 3\mathbf{k}) = 7 r ⋅ ( 5 i + 2 j − 3 k ) = 7 r ⋅ ( 5 i − 2 j − 3 k ) = 7 \mathbf{r} \cdot (5\mathbf{i} - 2\mathbf{j} - 3\mathbf{k}) = 7 r ⋅ ( 5 i − 2 j − 3 k ) = 7 r ⋅ ( 5 i + 2 j + 3 k ) = 7 \mathbf{r} \cdot (5\mathbf{i} + 2\mathbf{j} + 3\mathbf{k}) = 7 r ⋅ ( 5 i + 2 j + 3 k ) = 7 Browse the problem library